Preheat oven to 350° F / 175° C. Butterfly the chicken breasts using a sharp knife to carefully cut into one side until it opens like a book. Season the interior with salt and pepper, and coat with 1 teaspoon mustard. Top with a slice of cheese, then a slice of prosciutto or ham. Close and secure with string or toothpicks. Dredge this chicken preparation in flour, then dip in the beaten egg, and then roll in breadcrumbs. Repeat for the other breasts. Bake in a dish atop parchment paper or foil for 35 to 45 minutes, or until the parcels are firm to the touch, and juices running from the chicken are clear and no longer pink, or a thermeter reaches 180° F/80° C.
Heat the wine in a saucepan over high heat and reduce by half. Add the stock, bring to a boil and reduce to a simmer. Keep warm until ready to add to the below sauce. (Don’t skip this step, your sauce will break.)
In another saucepan, make a roux by melting the butter in a saucepan over medium heat until bubbly. Whisk in the flour and continue to whisk for eight to 10 minutes, until it smells like popcorn. Add the cold milk and whisk in completely. Whisk in the wine-stock mixture and season with salt and pepper. Add in the grated cheese and stir until melted through. Adjust consistency by adding more stock if sauce is too thick.
Remove the string from the chicken. Top with the sauce.